## Algebra For SBI PO : Set – 27

D.1-5) : In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

I. 20x2 – 67x + 56 = 0

II) 56y2 – 67y + 20 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(a)

20x2 – 35x – 32x + 56 = 0

or 5x (4x – 7) – 8 (4x – 7) = 0

or (5x – 8) (4x – 7) = 0

x =8/5,7/4

56y2 – 32y – 35y + 20 = 0

or 8y (7y – 4) – 5 (7y – 4) = 0

or (8y – 5) (7y – 4) = 0

∴x=5/8,4/7

x > y

2. I. x4 = 65536

II) y = ∛4096

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(d)

x4 = 65536

x = +16

II. y = ∛4096

y = 16

3) I. 2x2 + 11x – 40 = 0

II) 4y2 – 27y + 44 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(c)

2x2 + 16x – 5x – 40 = 0

or 2x (x + 8) – 5 (x + 8) = 0

or (2x – 5) (x + 8) = 0

∴x=5/2,-8

II. 4y2 – 16y – 11y + 44 = 0

or 4y (y – 4) – 11 (y – 4) = 0

or (4y – 11) (y – 4) = 0

y = 4, 11/4

∴x<y

4) I. 7x = 4y + 85

II) y = ∛17576

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(a)

7x= 4y + 85

or 7x = 4 × 26 + 85 (Put y = 26)

∴x= 189/7 = 27

II. y = ∛17576

y = 26

x > y

5) I. x2 = 14641

II) y = √14641

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(d)

x2 = 14641

x = ±121

II. y = √14641

y = 121

D.6-10): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or if there is no relation between ‘x’ and ‘y’.

6) I. x2 + 42 = 13x

II) y=∜1296

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(b)

x2 + 42 = 13x

or x2 – 13x + 42 = 0

or x2 – 7x – 6x + 42 = 0

or x(x – 7) – 6(x – 7) = 0

or (x – 6) (x – 7) = 0

x = 6, 7

II. y = ∜1296

y = 6

7) I. x2 + x – 2 = 0

II) y2 + 7y + 12 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(a)

I. x2 + x – 2 = 0

or x2 + 2x – x – 2 = 0

or x(x + 2) – 1(x + 2) = 0

or (x – 1) (x + 2) = 0

x = 1, – 2

II. y2 + 7y + 12 = 0

or y2 + 3y + 4y + 12 = 0

or y(y + 3) + 4(y + 3) = 0

or (y + 3) (y + 4) = 0

y = -3, -4 x > y

8. I. 3x2 – 23x + 40 = 0

II) 2y2 – 23y + 66 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(c)

3x2 – 23x + 40 = 0 or 3x2 – 15x – 8x + 40 = 0

or 3x (x – 5) – 8 (x – 5) = 0

or (3x – 8) (x – 5) = 0 8

x = 5, 8/3

II. 2y2 – 23y + 66 = 0

or 2y2 – 12y – 11y + 66 = 0

or 2y (y – 6) -11 (y – 6) = 0

or (y – 6) (2y – 11) = 0

y = 6,11/2

x<y

9. I. 15x2 – 46x + 35 = 0

II) 4y2 – 15y + 14 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(c)

I. 15x2 – 25x – 21x + 35 = 0

or 5x (3x – 5) – 7 (3x – 5) = 0

or (5x – 7) (3x – 5) = 0

∴x= 7/5,5/3

4y2 – 8y – 7y + 14 = 0

or 4y (y – 2) – 7 (y – 2) = 0

or (4y – 7) (y – 2) = 0

y = 2, 7/4

x < y

10. I. x2 + 5x – 6 = 0

II) 2y2 – 11y + 15 = 0

(a) if x > y

(b) if x ≥ y

(c) if x < y

(d) if x ≤ y

(e) if x = y or no relationship can be established.

(c)

x2 – x + 6x -6 = 0 or x(x – 1) + 6(x – 1) = 0

or (x – 1) (x + 6) = 0 x = 1, -6

II. 2y2 – 6y – 5y + 15 = 0

or 2y (y – 3) – 5 (y – 3) = 0

or (y – 3) (2y – 5) = 0

y = 3,5

x < y